Fitness drivers of division of labor in vertebrates
- Department of Ecology, Evolution and Environmental Biology, Columbia University, United States
Figures
Figure 1
Diagram of the scheduling executed per breeding cycle.
(1) A breeder reproduces. Its productivity depends on the cumulative level of brood care provided by the group during the previous breeding cycle. Maximum productivity is achieved when different helping tasks are performed to a similar extent. (2) Subordinates may disperse to become floaters, or they may stay in the group and help (1). Dispersers/floaters may join a random group to become subordinates. (3) Subordinates in the group (both natal and immigrant individuals) either work to provision to the breeder’s offspring or display defensive forms of help. (4) Individuals survive contingent on group-living benefits and dispersal costs, as well as the cost of defensive activities. (5) If a breeder dies, helpers in the group and a sample of floaters compete for the breeding position. Individuals still alive ascend one age class, and the cycle starts all over (i.e. next breeding cycle).
Figure 2
Effect of environmental quality on alloparental care and division of labor.
The evolutionary equilibria for phenotypic levels of helping and task specialization are shown at three different levels of environmental quality, ranging from benign (m = 0.1) to harsh (m = 0.3), and for three different levels of cost of help on survival (light blue, xh = 3; blue, xh = 5; and dark blue,xh = 7), across 20 replicas. The vertical axis represents the expressed task allocation between a defensive task with a cost to survival versus a work task with a cost to their dominance rank. The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (▲) or when no restrictions were introduced to the task performed by the group members (〇). In each environment, additional details are given on the selective forces that play a role in the evolution of help and task specialization: help can only evolve by kin selection (KS), group augmentation (GA), or both (KS + GA). Additional details are provided in Table 2. For variation in yh values instead, see Appendix 1. All input parameter values are described in Table 1.
Figure 3
Evolved reaction norms to age on the display of task specialization.
The evolutionary equilibria for the reaction norms of task specialization are shown at five different levels of environmental quality, ranging from benign (m = 0.1, purple) to harsh (m = 0.3, yellow), and xh = 5. (A) γR > 0 signifies that individuals increase the probability of performing work tasks with dominance (defense → work), whereas γR < 0 signifies that individuals increase the probability of performing defensive tasks with dominance (work → defense). The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (▲), or when no restrictions were introduced to the task performed by the group members (〇). Results show that at equilibrium when division of labor evolves, individuals increase the probability of performing their preferred task (circles), when increasing their dominance value. (B) Evolved reaction norms to dominance value with average γ0 and γR across 20 replicas for varying quality environments. All parameter values described in Table 1.
Appendix 1—figure 1
Effect of variation in the cost of help to rank.
The evolutionary equilibria for phenotypic levels of helping and task specialization are shown at three different levels of environmental quality, ranging from benign (m = 0.1) to harsh (m = 0.3), and for three different levels of cost of help on rank (light green, yh = 0.05; medium-light green, yh = 0.1; medium-dark green, yh = 0.5; and dark green, yh = 1), across 20 replicas. The vertical axis expresses the probability of individuals choosing a defensive task with a cost to survival versus a work task with a cost to their dominance rank. The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (▲), or when no restrictions were introduced to the task performed by the group members (〇). In each environment, additional details are given on the selective forces that play a role in the evolution of help and task specialization: help can only evolve by kin selection (KS), group augmentation (GA), or both (KS + GA). Input parameters are the same as in Figure 2, except for fixed value of xh = 5 and variation in yh. Additional details are provided in Appendix 1—table 1.
Appendix 2—figure 1
Effect of increasing the baseline survival x0 to favor the evolution of division of labor under only kin selection.
The evolutionary equilibria for levels of helping and task specialization are shown at three different levels of environmental quality, ranging from benign (m = 0.1) to harsh (m = 0.3), and for three different levels of cost of help on survival (light blue, xh = 3; blue, xh = 5; and dark blue, xh = 7). The vertical axis represents the expressed task allocation between a defensive task with a cost to survival versus a work task with a cost to dominance. The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (▲), or when no restrictions were introduced to the task performed by the group members (〇). Input parameters are the same as in Figure 2 (where x0 = 1.5) except for x0 = 4.5 and x0 = 10 (higher survival for all individuals irrespective of group membership or environment; Table 1). Additional details are provided in Appendix 2—table 1.
Appendix 2—figure 2
Effect of reducing the incentives to disperse to favor the evolution of division of labor under only kin selection.
An increase in incentives to remain philopatric was achieved by reducing f to 1 (f = 2 in Figure 2; Table 1). The evolutionary equilibria for levels of helping and task specialization are shown at three different levels of environment quality that range from benign (m = 0.1) to harsh (m = 0.3), and for three different levels of cost of help on survival (light blue, xh = 3; blue, xh = 5; and dark blue, xh = 7). The vertical axis represents the expressed task allocation between a defensive task with a cost to survival versus a work task with a cost to dominance. The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (▲), or when no restrictions were introduced to the task performed by the group members (〇). Other input parameters are the same as in Figure 2 (where x0 = 1.5) except for x0 = 4.5 and x0 = 10 (higher survival for all individuals irrespective of group membership or environment; Table 1). Additional details are provided in Appendix 2—table 2.
Appendix 2—figure 3
Effect of reducing within-group relatedness by half to mimic sexual reproduction.
A reduction in within-group relatedness was achieved by shuffling half of the philopatric newborns to another group in the kin selection (KS) and KS+ group augmentation (GA) implementations, and all for the GA implementation. The evolutionary equilibria for levels of helping and task specialization are shown at three different levels of environment quality that range from benign (m = 0.1) to harsh (m = 0.3), and for three different levels of cost of help on survival (light blue, xh = 3; blue, xh = 5; and dark blue, xh = 7). The vertical axis represents the expressed task allocation between a defensive task with a cost to survival versus a work task with a cost to dominance. The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (▲), or when no restrictions were introduced to the task performed by the group members (〇). Input parameters are the same as in Figure 2. Additional details are provided in Appendix 2—table 3.
Appendix 2—figure 4
Effect of obligatory division of labor in the emergence of task division under only kin selection fitness benefits.
For an increase in the productivity of the breeder, both kinds of task had to be performed to a similar extent at the group level. The evolutionary equilibria for levels of helping and task specialization are shown at three different levels of environment quality that range from benign (m = 0.1) to harsh (m = 0.3), and for three different levels of cost of help on survival (light blue, xh = 3; blue, xh = 5; and dark blue, xh = 7). The vertical axis represents the expressed task allocation between a defensive tasks with a cost to survival versus a work tasks with a cost to dominance. Breeder productivity was enhanced exclusively when both tasks were performed to a similar extent (obligatory division of labor; ▲), or simply when the task performed similarly by the group members (favorable division of labor; 〇). Input parameters are the same as in Figure 2 except for variation in kh (kh = 1 is default), βinit = 0.5, and kp = 0.5. Additional details are provided in Appendix 2—table 4.
Appendix 3—figure 1
Effect of adding a reaction norm of dispersal and immigration propensity to dominance value.
The evolutionary equilibria for phenotypic levels of helping and task specialization are shown at three different levels of environmental quality, ranging from benign (m = 0.1) to harsh (m = 0.3), and for three different levels of cost of help on survival (light blue, xh = 3; blue, xh = 5; and dark blue, xh = 7), across 20 replicas. The vertical axis represents the expressed task allocation between a defensive task with a cost to survival versus a work task with a cost to their dominance rank. The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (▲), or when no restrictions were introduced to the task performed by the group members (〇). In each environment, additional details are given on the selective forces that play a role in the evolution of help and task specialization: help can only evolve by kin selection (KS), group augmentation (GA), or both (KS + GA). Input parameters are the same as in Figure 2 with the addition of the β0 and βR. Additional details are provided in Appendix 3—table 1.
Appendix 4—figure 1
Effect of decreasing the benefits of group augmentation.
The evolutionary equilibria for phenotypic levels of helping and task specialization are shown at three different levels of environmental quality, ranging from benign (m = 0.1) to harsh (m = 0.3), and for three different levels of cost of help on survival (lightest blue, xh = 1, blue, xh = 3; dark blue, xh = 5; and darkest blue, xh = 7), across 20 replicas. The vertical axis expresses the probability of individuals choosing a defensive task with a cost to survival versus a work task with a cost to their dominance rank. The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (▲) or when no restrictions were introduced to the task performed by the group members (〇). In each environment, additional details are given on the selective forces that play a role in the evolution of help and task specialization: help can only evolve by kin selection (KS), group augmentation (GA), or both (KS + GA). Input parameters are the same as in Figure 2, except for fixed value of xn = 1 for the GA and KS + GA implementations. Additional details are provided in Appendix 4—table 1.
Tables
Table 1
Overview of notation.
Values conveyed for the genes are initial input values, and values given for the scaling parameters are fixed throughout the simulations. If more than one value is given, results are shown to display the effect of this parameter’s variation.
| Symbol | Meaning | Value |
|---|---|---|
| Genes | ||
| α | Genetic propensity to help | 0 |
| β | Genetic predisposition to disperse vs remain in a group | 1 |
| β0 | Intercept in the dispersal reaction norm | 1 |
| βR | Effect size of rank on dispersal propensity | 0 |
| γ0 | Intercept in the task specialization reaction norm | 0 |
| γR | Effect size of rank on task specialization | 0 |
| Scaling parameters | ||
| yh | Effect size of cost of help on dominance when performing ‘work tasks’ | 0.1* |
| xh | Effect size of cost of help in survival when performing ‘defensive tasks’ | 3 / 5 / 7* |
| xn | Effect size of the benefit of group size in survival | 0 / 3 |
| x0 | Intercept in the survival function | 1.5* |
| m | Baseline mortality | 0.1 – 0.3 |
| f | Mean number of groups a floater samples for becoming a breeder | 2* |
| km | Deviation from a perfect split in the need of both defense and work tasks | 0.1 |
| kh | Effect size of the cumulative help of subordinates on the fecundity of the breeder | 1* |
| k0 | Fecundity of the breeder in the absence of help | 1 |
| μ | Mutation rate | 0.05 |
| σμ | Mutation step size | 0.04 |
| Nb | Number of breeding territories | 5000 |
| Phenotypic traits | ||
| H | Level of help of either kind provided to the breeder H = α, applying boundary of 0 for negative numbers. We express cumulative level of help given in a group as ∑Hi | |
| D | Dispersal propensity D = β, applying boundaries between 0 and 1 | |
| R | Dominance value, applying boundary of 0 for negative numbers | |
| T | Probability of choosing ‘defensive task’ vs ‘work task’ | |
| S | Survival probability | |
| K | Fecundity of the breeder | |
| Variables | ||
| t | Age | |
| N | Emergent group size | |
| Nf | Total number of floaters | |
| Nf,b | Number of floaters bidding for a breeding position, given by Nf,b = | |
-
*
Additional values of these parameters are discussed in the Appendices. A broader parameter landscape was explored but not included in the manuscript.
Table 2
Supplementary data for Figure 2.
Mean values are shown for dispersal propensity, survival probability, group size (± SD), number of floaters (± SD), ratio between helpers’ and floaters’ dominance value (helpers’ rank/floaters’ rank ± SD) and within-group relatedness for three environmental qualities ranging from benign (m = 0.1) to harsh (m = 0.3) across 20 replicas. Selective forces at play include kin selection (KS), group augmentation (GA), or both (KS + GA). The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (DoL), or when no restrictions were introduced to the task performed by the group members (No DoL).
| KS | GA | KS +GA | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | |||||||||||||
| DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | ||||
| Dispersal | 0.95 | 0.92 | 0.94 | 0.90 | 0.91 | 0.84 | 0.01 | 0.01 | 0.11 | 0.10 | 0.37 | 0.33 | 0.07 | 0.07 | 0.22 | 0.22 | 0.43 | 0.52 | |||
| Survival | 0.74 | 0.74 | 0.65 | 0.65 | 0.57 | 0.57 | 0.90 | 0.90 | 0.79 | 0.79 | 0.66 | 0.67 | 0.89 | 0.89 | 0.77 | 0.77 | 0.65 | 0.65 | |||
| Group size | 1.16±0.16 | 1.34±0.30 | 1.14±0.12 | 1.25±0.19 | 1.14±0.08 | 1.29±0.11 | 9.85±0.08 | 9.83±0.05 | 6.94±0.43 | 7.52±0.41 | 3.04±0.35 | 3.40±0.36 | 16.42±0.10 | 16.55±0.07 | 6.42±0.14 | 6.61±0.11 | 2.95±0.25 | 2.83±0.05 | |||
| Number of floaters | 14280±1352 | 15616±2322 | 9778±711 | 10352±1082 | 6956±330 | 7482±395 | 297±23 | 297±22 | 3512±104 | 3428±101 | 5925±137 | 5905±122 | 5956±121 | 5968±107 | 7523±252 | 7853±201 | 7353±1173 | 9741±224 | |||
| Rank ratio helpers vs floaters | 0.91±0.27 | 0.94±0.22 | 0.85±0.24 | 0.88±0.25 | 0.76±0.27 | 0.75±0.12 | 1.05±0.06 | 1.06±0.06 | 1.05±0.04 | 1.06±0.04 | 1.03±0.06 | 1.03±0.06 | 1.02±0.03 | 1.03±0.03 | 1.00±0.04 | 1.00±0.04 | 0.97±0.07 | 0.89±0.06 | |||
| Relatedness | 0.37 | 0.36 | 0.54 | 0.52 | 0.73 | 0.71 | 0 | 0 | 0 | 0 | 0 | 0 | 0.56 | 0.57 | 0.57 | 0.57 | 0.65 | 0.60 | |||
Appendix 1—table 1
Supplementary data for the effect of variation in the cost of help to rank shown in Appendix 1—figure 1.
Mean values are shown for dispersal propensity, survival probability, group size (± SD), number of floaters (± SD), ratio between helpers’ and floaters’ dominance value (± SD) and within-group relatedness for three environmental qualities ranging from benign (m = 0.1) to harsh (m = 0.3) across 20 replicas. Selective forces at play include kin selection (KS), group augmentation (GA), or both (KS + GA). The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (DoL), or when no restrictions were introduced to the task performed by the group members (No DoL).
| KS | GA | KS + GA | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | |||||||||||||
| DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | ||||
| Dispersal | 0.95 | 0.92 | 0.94 | 0.92 | 0.93 | 0.90 | 0.01 | 0.01 | 0.11 | 0.10 | 0.45 | 0.33 | 0.07 | 0.07 | 0.22 | 0.22 | 0.43 | 0.48 | |||
| Survival | 0.74 | 0.74 | 0.65 | 0.65 | 0.57 | 0.57 | 0.90 | 0.90 | 0.79 | 0.79 | 0.66 | 0.67 | 0.89 | 0.89 | 0.77 | 0.77 | 0.66 | 0.65 | |||
| Group size | 1.18±0.21 | 1.30±0.30 | 1.14±0.15 | 1.20±0.19 | 1.11±0.11 | 1.19±0.16 | 9.83±0.07 | 9.84±0.06 | 6.85±0.26 | 7.52±0.19 | 2.68±0.61 | 3.41±0.20 | 16.41±0.09 | 16.53±0.08 | 6.25±0.20 | 6.55±0.15 | 3.02±0.18 | 2.87±0.11 | |||
| Number of floaters | 14519±1452 | 15396±2143 | 9753±820 | 10234±1006 | 6838±421 | 7162±558 | 299±26 | 293±23 | 3514±98 | 3441±103 | 6169±548 | 5905±132 | 5930±128 | 5982±107 | 7438±158 | 7774±258 | 7594±1560 | 8704±1139 | |||
| Rank ratio helpers vs floaters | 0.80±0.20 | 0.83±0.20 | 0.77±0.25 | 0.71±0.35 | 0.77±0.31 | 0.66±0.33 | 1.05±0.06 | 1.05±0.05 | 1.05±0.02 | 1.05±0.03 | 1.03±0.03 | 1.02±0.04 | 1.02±0.02 | 1.03±0.02 | 1.00±0.02 | 1.00±0.02 | 0.94±0.05 | 0.95±0.06 | |||
| Relatedness | 0.38 | 0.36 | 0.53 | 0.52 | 0.74 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.57 | 0.57 | 0.57 | 0.64 | 0.62 | |||
Appendix 2—table 1
Supplementary data for the effect of increasing the baseline survival x0 to favor the evolution of division of labor under only kin selection shown in Appendix 2—figure 1.
Mean values are shown for dispersal propensity, survival probability, group size (± SD), number of floaters (± SD), ratio between helpers’ and floaters’ dominance value (± SD) and within-group relatedness for three environmental qualities ranging from benign (m = 0.1) to harsh (m = 0.3) across 20 replicas. Results are shown for x0 = 1.5 (default), x0 = 3.5, and x0 = 10. The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (DoL), or when no restrictions were introduced to the task performed by the group members (No DoL).
| x0 = 1.5 | x0 = 4.5 | x0 = 10 | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | |||||||||||||
| DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | ||||
| Dispersal | 0.95 | 0.92 | 0.94 | 0.90 | 0.91 | 0.84 | 0.84 | 0.85 | 0.89 | 0.86 | 0.89 | 0.85 | 0.79 | 0.83 | 0.88 | 0.85 | 0.9 | 0.85 | |||
| Survival | 0.74 | 0.74 | 0.65 | 0.65 | 0.57 | 0.57 | 0.89 | 0.89 | 0.79 | 0.79 | 0.69 | 0.69 | 0.90 | 0.90 | 0.80 | 0.80 | 0.70 | 0.70 | |||
| Group size | 1.16±0.16 | 1.34±0.30 | 1.14±0.12 | 1.25±0.19 | 1.14±0.08 | 1.29±0.11 | 3.02±0.33 | 3.14±0.14 | 1.61±0.26 | 1.86±0.21 | 1.33±0.13 | 1.50±0.09 | 4.19±0.19 | 3.75±0.20 | 1.68±0.22 | 1.96±0.07 | 1.31±0.11 | 1.49±0.07 | |||
| Number of floaters | 14280±1352 | 15616±2322 | 9778±711 | 10352 ±1082 | 6956±330 | 7482±395 | 53241±5074 | 61820±1393 | 22911±2167 | 25655±1903 | 12672±836 | 13848±548 | 59534±3345 | 65170±2536 | 23585±1799 | 27291±560 | 12901±775 | 14293±574 | |||
| Rank ratio helpers vs floaters | 0.91±0.27 | 0.94±0.22 | 0.85±0.24 | 0.88±0.25 | 0.76±0.27 | 0.75±0.12 | 0.97 ±0.06 | 0.95±0.09 | 0.90±0.16 | 0.85±0.11 | 0.81±0.12 | 0.85±0.09 | 1.00±0.05 | 0.99±0.06 | 0.98±0.13 | 0.93±0.07 | 0.89±0.19 | 0.84±0.13 | |||
| Relatedness | 0.37 | 0.36 | 0.54 | 0.52 | 0.73 | 0.71 | 0.15 | 0.15 | 0.28 | 0.28 | 0.45 | 0.44 | 0.17 | 0.15 | 0.27 | 0.27 | 0.44 | 0.43 | |||
Appendix 2—table 2
Supplementary data for the effect of reducing the incentives to disperse to favor the evolution of division of labor under only kin selection shown in Appendix 2—figure 2.
The increased incentive was achieved by reducing the parameter f that signifies the mean number of groups a floater samples for becoming a breeder from 2 (default) to 1. Mean values are shown for dispersal propensity, survival probability, group size (± SD), number of floaters (± SD), ratio between helpers’ and floaters’ dominance value (± SD) and within-group relatedness for three environmental qualities ranging from benign (m = 0.1) to harsh (m = 0.3) across 20 replicas. Results are shown for x0 = 1.5 (default), x0 = 3.5, and x0 = 10. The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (DoL), or when no restrictions were introduced to the task performed by the group members (No DoL).
| x0 = 1.5 | x0 = 4.5 | x0 = 10 | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | |||||||||||||
| DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | ||||
| Dispersal | 0.82 | 0.75 | 0.79 | 0.79 | NA | NA | 0.23 | 0.24 | 0.49 | 0.50 | 0.72 | 0.68 | 0.25 | 0.25 | 0.44 | 0.47 | 0.49 | 0.66 | |||
| Survival | 0.74 | 0.74 | 0.65 | 0.65 | 0 | 0 | 0.89 | 0.89 | 0.79 | 0.79 | 0.69 | 0.69 | 0.90 | 0.90 | 0.80 | 0.80 | 0.70 | 0.70 | |||
| Group size | 1.90±1.07 | 2.34±1.26 | 1.71±0.62 | 1.75±0.75 | 0 | 0 | 13.09±0.23 | 13.35±0.40 | 4.84±0.38 | 4.90±0.08 | 2.04±0.06 | 2.33±0.05 | 14.29±0.26 | 14.59±0.16 | 5.17±0.37 | 5.30±0.08 | 3.10±0.26 | 2.47±0.05 | |||
| Number of floaters | 14116±972 | 14468±1058 | 9986±773 | 9957±859 | 0 | 0 | 18182±894 | 19426±1767 | 18440±1678 | 19531±337 | 13682±154 | 14236±185 | 21746±639 | 22100±361 | 16541±1838 | 18755±393 | 9839±265 | 14274±515 | |||
| Rank ratio helpers vs floaters | 1.10±0.43 | 1.01±0.19 | 0.96±0.37 | 1.04±0.59 | NA | NA | 0.98±0.03 | 0.98±0.03 | 0.93±0.04 | 0.96±0.04 | 0.86±0.09 | 0.86±0.07 | 0.99±0.02 | 0.98±0.03 | 0.98±0.05 | 0.97±0.04 | 1.00±0.05 | 0.89±0.08 | |||
| Relatedness | 0.40 | 0.39 | 0.55 | 0.56 | NA | NA | 0.32 | 0.32 | 0.37 | 0.36 | 0.46 | 0.46 | 0.29 | 0.29 | 0.38 | 0.36 | 0.52 | 0.46 | |||
Appendix 2—table 3
Supplementary data for effect of reducing within-group relatedness by half to mimic sexual reproduction shown in Appendix 2—figure 3.
Mean values are shown for dispersal propensity, survival probability, group size (± SD), number of floaters (± SD), ratio between helpers’ and floaters’ dominance value (± SD) and within-group relatedness for three environmental qualities ranging from benign (m = 0.1) to harsh (m = 0.3) across 20 replicas. Selective forces at play include kin selection (KS), group augmentation (GA), or both (KS + GA). The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (DoL), or when no restrictions were introduced to the task performed by the group members (No DoL).
| KS | GA | KS + GA | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | |||||||||||||
| DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | ||||
| Dispersal | 0.94 | 0.93 | 0.93 | 0.90 | 0.91 | 0.88 | 0.01 | 0.01 | 0.11 | 0.10 | 0.37 | 0.33 | 0.02 | 0.02 | 0.11 | 0.11 | 0.41 | 0.50 | |||
| Survival | 0.74 | 0.74 | 0.65 | 0.65 | 0.57 | 0.57 | 0.90 | 0.90 | 0.79 | 0.79 | 0.66 | 0.67 | 0.90 | 0.90 | 0.79 | 0.79 | 0.66 | 0.65 | |||
| Group size | 1.20±0.19 | 1.29±0.27 | 1.16±0.12 | 1.26±0.18 | 1.14±0.08 | 1.22±0.14 | 9.85±0.08 | 9.83±0.05 | 6.94±0.43 | 7.52±0.41 | 3.04±0.35 | 3.40±0.36 | 18.37±0.10 | 18.54±0.09 | 7.66±0.15 | 7.86±0.21 | 3.16±0.53 | 2.78±0.09 | |||
| Number of floaters | 14491±1329 | 15139±2030 | 9820±682 | 10300±1004 | 6869±291 | 7123±486 | 297±23 | 297±22 | 3512±104 | 3428±101 | 5925±137 | 5905±122 | 2216±74 | 2218±83 | 4164±124 | 4179±119 | 7327±1378 | 9020±346 | |||
| Rank ratio helpers vs floaters | 0.90±0.24 | 0.98±0.26 | 0.90±0.27 | 0.91±0.22 | 0.85±0.26 | 0.93±0.25 | 1.05±0.06 | 1.06±0.06 | 1.05±0.04 | 1.06±0.04 | 1.03±0.06 | 1.03±0.06 | 1.06±0.03 | 1.06±0.03 | 1.02±0.04 | 1.03±0.04 | 0.95±0.07 | 0.94±0.06 | |||
| Relatedness | 0.18 | 0.20 | 0.27 | 0.26 | 0.36 | 0.36 | 0 | 0 | 0 | 0 | 0 | 0 | 0.30 | 0.31 | 0.31 | 0.31 | 0.32 | 0.30 | |||
Appendix 2—table 4
Supplementary data for the effect of obligatory division of labor in the emergence of task division under only kin selection fitness benefits shown in Appendix 2—figure 4.
Mean values are shown for dispersal propensity, survival probability, group size (± SD), number of floaters (± SD), ratio between helpers’ and floaters’ dominance value (± SD), and within-group relatedness for three environmental qualities ranging from benign (m = 0.1) to harsh (m = 0.3) across 20 replicas. The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (DoL favored), or when division of labor was required to increase the breeder’s productivity (DoL obligatory). Note that for kh = 7, m = 0.3 implementation ‘DoL favored’, only one replicate survived, hence SD is not defined.
| kh = 1 | kh = 4 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | |||||||||
| DoL obligatory | DoL favored | DoL obligatory | DoL favored | DoL obligatory | DoL favored | DoL obligatory | DoL favored | DoL obligatory | DoL favored | DoL obligatory | DoL favored | |||
| Dispersal | 0.97 | 0.92 | 0.97 | 0.91 | NA | NA | 0.97 | 0.83 | 0.97 | 0.8 | NA | NA | ||
| Survival | 0.74 | 0.74 | 0.65 | 0.65 | 0 | 0 | 0.74 | 0.74 | 0.65 | 0.65 | 0 | 0 | ||
| Group size | 1.07±0.01 | 1.29±0.20 | 1.05±0.01 | 1.21±0.12 | NA | NA | 1.07±0.01 | 3.42±0.09 | 1.05±0.01 | 3.02±0.07 | NA | NA | ||
| Number of floaters | 13560 ±127 | 15323 ±1661 | 9207±133 | 10168 ±728 | NA | NA | 13591±134 | 60761±501 | 9201±127 | 40928±451 | NA | NA | ||
| Rank ratio helpers vs floaters | 1.01±0.05 | 0.91±0.11 | 1.01±0.05 | 0.84±0.15 | NA | NA | 1.00±0.04 | 0.82±0.02 | 1.01±0.05 | 0.76±0.01 | NA | NA | ||
| Relatedness | 0.37 | 0.37 | 0.53 | 0.52 | NA | NA | 0.37 | 0.32 | 0.54 | 0.42 | NA | NA | ||
| kh = 7 | kh = 10 | |||||||||||||
| m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | |||||||||
| DoL obligatory | DoL favored | DoL obligatory | DoL favored | DoL obligatory | DoL favored | DoL obligatory | DoL favored | DoL obligatory | DoL favored | DoL obligatory | DoL favored | |||
| Dispersal | 0.95 | 0.87 | 0.97 | 0.85 | NA | 0.83 | 0.61 | 0.89 | 0.67 | 0.87 | NA | 0.86 | ||
| Survival | 0.73 | 0.74 | 0.65 | 0.65 | 0 | 0.57 | 0.71 | 0.74 | 0.63 | 0.65 | NA | 0.57 | ||
| Group size | 1.24±0.65 | 4.36±0.14 | 1.05±0.01 | 3.81±0.11 | NA | 3.29 | 5.62±3.31 | 5.01±0.21 | 3.00±1.43 | 4.36±0.15 | NA | 3.9±0.10 | ||
| Number of floaters | 13835±995 | 110167±935 | 9204±133 | 77579±642 | NA | 56608 | 21631±6556 | 161169±1227 | 13833±4002 | 115694±859 | NA | 87503 ±642 | ||
| Rank ratio helpers vs floaters | 1.00±0.04 | 0.82±0.02 | 1.01±0.04 | 0.77±0.02 | NA | 0.69 | 1.00±0.03 | 0.83±0.02 | 1.00 ±0.03 | 0.76±0.01 | NA | 0.71±0.02 | ||
| Relatedness | 0.39 | 0.31 | 0.54 | 0.4 | NA | 0.48 | 0.42 | 0.29 | 0.55 | 0.39 | NA | 0.47 | ||
Appendix 3—table 1
Supplementary data for the effect of adding a reaction norm of dispersal and immigration propensity to dominance value shown in Appendix 3—figure 1.
Mean values are shown for dispersal propensity, survival probability, group size (± SD), number of floaters (± SD), ratio between helpers’ and floaters’ dominance value (± SD) and within-group relatedness for three environmental qualities ranging from benign (m = 0.1) to harsh (m = 0.3) across 20 replicas. Selective forces at play include kin selection (KS), group augmentation (GA), or both (KS + GA). The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (DoL), or when no restrictions were introduced to the task performed by the group members (No DoL).
| KS | GA | KS +GA | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | |||||||||||||
| DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | ||||
| Dispersal | 1.00 | 0.94 | 1.00 | 0.96 | NA | NA | 0.00 | 0.00 | 0.16 | 0.15 | 0.67 | 0.51 | 0.08 | 0.08 | 0.20 | 0.20 | 0.43 | 0.45 | |||
| βR | –3.71 | –3.17 | –4.27 | –4.18 | NA | NA | 3.99 | 3.99 | –0.30 | –0.48 | –4.61 | –4.52 | 2.71 | 2.72 | 0.67 | 2.17 | 2.45 | 3.49 | |||
| Survival | 0.74 | 0.74 | 0.65 | 0.65 | NA | NA | 0.90 | 0.90 | 0.78 | 0.78 | 0.65 | 0.64 | 0.89 | 0.89 | 0.77 | 0.77 | 0.66 | 0.65 | |||
| Group size | 1.00±0.00 | 1.27±0.39 | 1.01±0.06 | 1.12±0.22 | NA | NA | 9.76±0.08 | 9.75±0.11 | 6.15±0.78 | 6.77±0.99 | 1.87±0.57 | 2.44±0.16 | 16.21±0.10 | 16.23±0.10 | 6.60±0.16 | 6.85±0.17 | 3.13±0.38 | 3.15±0.06 | |||
| Number of floaters | 13928±123 | 15486±2148 | 9477±236 | 9943±928 | NA | NA | 25±9 | 26±9 | 4630±493 | 4740±1303 | 7350±504 | 7367±730 | 6408±148 | 6537±144 | 7059±188 | 7190±177 | 8055±1161 | 8935±150 | |||
| Rank ratio helpers vs floaters | 0.47±0.16 | 0.98±1.18 | 0.58±0.27 | 0.45±0.05 | NA | NA | 5.70±0.43 | 5.76±0.44 | 0.55±0.06 | 0.51±0.07 | 0.62±0.12 | 0.55±0.02 | 5.91±0.19 | 6.07±0.18 | 1.83±0.45 | 2.43±0.48 | 1.91±0.17 | 2.06±0.12 | |||
| Relatedness | 0.31 | 0.34 | 0.31 | 0.30 | NA | NA | 0 | 0 | 0 | 0 | 0 | 0 | 0.37 | 0.37 | 0.48 | 0.43 | 0.42 | 0.36 | |||
Appendix 4—table 1
Supplementary data for the effect of decreasing the benefits of group augmentation shown in Appendix 4—figure 1.
Mean values are shown for dispersal propensity, survival probability, group size (± SD), number of floaters (± SD), ratio between helpers’ and floaters’ dominance value (± SD), and within-group relatedness for three environmental qualities ranging from benign (m = 0.1) to harsh (m = 0.3) across 20 replicas. Selective forces at play include kin selection (KS), group augmentation (GA), or both (KS + GA). The optimum breeder productivity per unit of help provided was either when both tasks were performed to a similar extent, potentially selecting for division of labor (DoL), or when no restrictions were introduced to the task performed by the group members (No DoL).
| KS | GA | KS + GA | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | m = 0.1 | m = 0.2 | m = 0.3 | |||||||||||||
| DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | DoL | No DoL | ||||
| Dispersal | 0.93 | 0.90 | 0.92 | 0.89 | 0.90 | 0.84 | 0.01 | 0.01 | 0.22 | 0.15 | 0.62 | 0.46 | 0.07 | 0.07 | 0.22 | 0.22 | 0.53 | 0.50 | |||
| Survival | 0.74 | 0.74 | 0.65 | 0.65 | 0.57 | 0.57 | 0.90 | 0.90 | 0.77 | 0.78 | 0.63 | 0.65 | 0.89 | 0.89 | 0.77 | 0.77 | 0.64 | 0.64 | |||
| Group size | 1.24±0.20 | 1.43±0.30 | 1.18±0.13 | 1.29±0.18 | 1.16±0.07 | 1.30±0.09 | 9.83±0.06 | 9.81±0.06 | 5.25±1.52 | 6.23±1.09 | 2.13±0.90 | 2.91±0.93 | 16.18±0.22 | 16.38±0.13 | 6.51±0.08 | 6.66±0.06 | 2.64±0.05 | 2.89±0.06 | |||
| Number of floaters | 14962±1673 | 16240±2289 | 9998±731 | 10620±1049 | 7015±311 | 7518±356 | 303±25 | 301±24 | 4461±1742 | 3843±1109 | 6590±627 | 6255±545 | 5791±180 | 5915±121 | 7758±185 | 7880±181 | 9138±133 | 9361±169 | |||
| Rank ratio helpers vs floaters | 0.89±0.22 | 0.92±0.18 | 0.82±0.21 | 0.86±0.22 | 0.74±0.24 | 0.75±0.11 | 1.05±0.05 | 1.05±0.06 | 1.05±0.02 | 1.05±0.02 | 1.00±0.02 | 1.00±0.03 | 1.02±0.01 | 1.01±0.02 | 0.96±0.02 | 0.97±0.02 | 0.82±0.01 | 0.87±0.01 | |||
| Relatedness | 0.37 | 0.36 | 0.53 | 0.52 | 0.73 | 0.71 | 0 | 0 | 0 | 0 | 0 | 0 | 0.57 | 0.56 | 0.57 | 0.57 | 0.61 | 0.61 | |||
Author response table 1
| task | help | dispersal | survival | relatedness | |
|---|---|---|---|---|---|
| m=0.1 | 0.01 | 6.19 | 0.88 | 0.74 | 0.37 |
| m=0.3 | 0.04 | 5.18 | 0.87 | 0.57 | 0.71 |
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Fitness drivers of division of labor in vertebrates
eLife 14:RP105501.
https://doi.org/10.7554/eLife.105501.5
